Posts: 2,247
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Hi All,
Valentin Albillo has published on his web site an HP-71B BASIC program that calculates the minimax coefficients of polynomials that pass through a discrete set of data. As I find myself interested in the algorithms used to evaluate basic transcendental functions, Valentin's approach comes across as very practical and useful. He provides a minimax polynomial that is very easy to evaluate.
I would like very much to obtain references for the algorithms behind the minimax polynomial fit. Links to web sitss or references to books are most appreciated.
Namir
Edited: 6 Sept 2006, 9:35 p.m.
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Hi, Namir:
Best regards from V.
Posts: 2,247
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Joined: Jun 2005
Excellent Valentin. Many many thanks for these references. I have tried coding (using Excel VBA so far) different methods to evaluate e^x, the basic trig functions and their inverses. The minimax polyomial that you showed in a previous post is the most practical for a handheld calculator (as an exercise of course). I have used the approximation by summing the products of constants coefficients with shifted Chebyshev polynomials. While they work ok in VBA (or any other high-level langauge), they are no practical to implement on a vintage programmable calculator like the HP-67.
Again, thanks for the references.
Namir